A Numerical anlysis of Resin Transfer Molding

The aim of this work is to study a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. The proposed model is 2-D, the chemical reactivity of the fluid is accounted with the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a solution of the proposed mathematical model.The aim of this work is to study a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. The proposed model is 2-D, the chemical reactivity of the fluid is accounted with the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a solution of the proposed mathematical model

Numerical approximation of an identification problem in porous media

When the ground is accidentally polluted with a volatile organic contaminant, it is important to know the amount of this contaminant in liquid form, in this paper it is shown that the concentration in the liquid phase of the volatile organic contaminant can be identified by analyzing the gaseous phase and using inverse problem. In order to do that we consider an inverse problem.When the ground is accidentally polluted with a volatile organic contaminant, it is important to know the amount of this contaminant in liquid form, in this paper it is shown that the concentration in the liquid phase of the volatile organic contaminant can be identified by analyzing the gaseous phase and using inverse problem. In order to do that we consider an inverse problem

Simultaneous segmentation of the left and right heart ventricles in 3D cine MR images of small animals

New high resolution image techniques allow to capture the anatomy and movement of the heart of small animals. The availability of these in vivo images can be very useful for medical research, however the amount of generated data for large animal studies makes manual analysis a very tedious task. To cope with the problem of automatic analysis of these images, we propose the use of the Deformable Elastic Template method to perform automatic segmentation of the ventricles. To adapt the method to the specificities of high-resolution MRI, several improvements are presented, including an image-context dependent scheme for more robust segmentation. Qualitative results show that our method is able to correctly retrieve the heart’s contours in 3D. 1

Singular Perturbations For Heart Image Segmentation Tracking

In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously

Consistency, Stability, a-Priori and a-Posteriori Errors for Nonlinear Problems

In an abstract framework similar to the one developed in Crouzeix-Rappaz [2], we present a formalism which makes precise the notions of consistency and stability for the finite element approximation of nonlinear elliptic problems. The consistency is connected to the approximation by interpolation, whereas the stability follows from discrete inf-sup conditions of the linearized problem. Moreover, contrary to the method developed in [2], this formalism does not require us to invert the principal part of the operator and allows us to obtain a priori and a posteriori error estimates for strongly nonlinear problems

Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems

results Let X and Z be two Banach spaces the norm of which are respectively denoted by k \Delta kX and by k \Delta kZ . If L(X; Z) is the Banach space of all continuous linear operators from X into Z, we denote by kTkXZ = sup u2X;kuk X =1 kTukZ the norm of T 2 L(X; Z). If G : X ! Z is a C 1 -mapping from X into Z and if u 2 X , we denote by DG(u) the Fr'echet derivative of G at the point u. We begin to establish a result which is similar to one of them we find in Girault-Raviart [9]. Numerische Mathematik Electronic Edition -- page numbers may differ from the printed version page 214 of Numer. Math. 69: 213--231 (1994) Petrov-Galerkin methods 215 Theorem 1. Let G : X ! Z be a C 1 -mapping from X into Z and let w be an element of X. We assume (2:1) (i) DG(w) is an isomorphism from X onto Z, (2:2) (ii) kDG(w) \Gamma1 kZX kG(w)kZ ffi=2 where ffi ? 0 is such that (2:3) sup x2X;kw\Gammaxk X ffi kDG(w) \Gamma DG(x)kXZ (2kDG(w) \Gamma1 kZX ) \Gamma1 : Then there exists a..

Méthodes mathématiques pour l'analyse d'images médicales

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